OK, I have OS 10.12.6 on my late 2012 Mac Mini, and a Canon MX890 Inkjet Printer. I rarely (if ever) use Preview, but I just launched it, and successfully printed out a Jpeg Photo, and the first page of a PDF document. Not sure why you are having issues, especially when you can print with Libre.
How did you upgrade? I always use the Combo Updater when I do an "in Mac OS" upgrade. although sometimes I'll do a full installation of the most current Mac OS, and then "migrate back" my apps, settings, etc, from my latest SuperDuper! backup. Again, not sure if it will make a difference, but you can get the OS 10.12.6 Combo Updater from here:
https://support.apple.com/kb/DL1931?locale=en_US
You could install it, and see if it helps. Additionally, when you did your last "major" Mac OS upgrade. how did you do that? Myself, after making a final clean SuperDuper! backup of my stuff with the latest of that last Mac OS (for example, OS 10.11.6), and of course insuring that my third party apps will work with the new Mac OS (might have needed to upgrade some of those), I then restart my Mac from that SuperDuper! backup, use Disk Utility there to Erase and Format my internal drive (SSDs in my case), then do a fresh, clean, "virgin" installation of the new Mac OS (OS 10.12.1, in my case), and finally use Migration Assistant to "migrate"/copy needed stuff from that SuperDuper! backup.
So, when High Sierra comes out, and also obtaining (most likely) 6 needed updates for 6 of my critical apps, I'll follow that process when I upgrade from OS 10.12.6 to (most likely) OS 10.13.1. (For my last 2 such upgrades, I had to wait and apply the first ".1" OS update, as a couple of my upgrades for some of my critical third party apps were not ready when the initial new Mac OS arrived).
Also, for my disk cleanup/maintenance/repair tasks, besides doing a good amount of disk cleanup on my own, I use the venerable Onyx, and the excellent commercial product Tech Tool Pro. IN fact, I depend upon them for both of my Macs. Some folks here have made negative comments about CleanMyMac, but I really cannot speak to that.
Finally, what software are you using for your backups?